[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close7 ]% B0 Q9 b$ U' d% D) s. I) ~6 N
% n=input('请输入迭代次数：');6 F+ o9 T w4 m& h: V% V- B
% qujian=input('请输入初始区间：');5 ^6 L( N4 R! |6 B
n=100;/ P4 q6 r! c. x' N6 [& s0 Y0 ^
wucha=0.005;4 b9 a\" P7 v\" L5 J. \
qujian=[0 1];
2 V/ m1 t4 s3 p, F* M
a(1)=qujian(1);
1 w% Z, t/ f2 c1 }4 U% v/ b
b(1)=qujian(2);
, Y) U. H5 M: \/ S1 x G
a0=a(1);5 w! {0 U; \8 E; g1 v. u1 G5 I
b0=b(1);( p\" w/ g6 x9 g% H6 n) ]\" Y& s
x=qujian;
5 ]: d% e& q) I. g% Z7 S9 `9 }5 Q9 p
y=exp(x)+10*x-2;
; A- N, P% N) _! K3 Q: q
y1=y(1); %小于0
2 ]4 Y* p! C$ ?
y2=y(2); %大于0: q: }& J/ l0 v7 O% D( }9 U
for i=1:n %总迭代次数
! u; R5 ?* D1 L# f\" z4 q
c(i)=(a+b)/2;
4 E2 R2 L7 ?+ S P; H+ F1 q. S
f(i)=exp(c(i))+10*(c(i))-2;
* ^; a! z/ y. ^1 R# J
kesai_k(i)=(b-a)/2;( b+ s/ H+ i, U+ u2 s
if f(i)>0
' y% b! {2 I! j% x: ^2 o
b=c(i);
% N$ I, n5 X& L; Z7 y# {
b1(i)=c(i);3 N1 p. I& m( }& ]
a1(i)=a;0 v) o w$ h0 j# F1 W
elseif f(i)<0# U! M6 \+ G& ?# J6 A0 \: _
a=c(i);
3 A! R/ j/ @* Y0 M/ i$ B
a1(i)=c(i);0 N% B; C1 [) g8 I: d
b1(i)=b;
\" p: O; _' |. C8 c& ?& |% Y
elseif f(i)==0||kesai_k(i)<=wucha1 X& N k6 p M- z0 @
disp('精确值解为：');
- Z8 ^/ k d3 b# L. B: p
disp(c(i));/ r) D6 v, Z% B\" z8 ?
break;9 C. n, X9 c1 D, ]
end\" d! ~6 V4 C4 r& n2 n
end3 t9 O$ a) F$ U$ R2 E6 i0 R
disp('迭代次数：');
% T k0 P. U2 J- ?
fprintf('%d次\n\n',n);
7 p. j* b) y; L% k
fprintf('要求误差%f\n\n',wucha);
- n' Y- p% S$ A G; y: W z
disp('输出矩阵为：');' N. F\" h- ]- F U0 h$ g5 F
A=[a0 a1]';( A1 N) f% |) \& x8 I! u
B=[b0 b1]';
! r0 M5 X6 Z' e6 [. J1 N
format long
% e. z( h2 T% A! Q
data_out=[A B c' f' kesai_k']' N I; S1 B3 V y# u C0 |
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：
6 l$ X. r2 H& Y$ f+ N
0.0905/ L6 ^% f {, c6 S5 U; o4 N
% x0 o; i2 U/ G$ f$ h4 H: }6 U) t
迭代次数：1 m; \* g, q% D\" B' R
100次\" _2 N4 {3 v0 B; {
0 y- A; e' l% V, [0 `7 Y$ R
要求误差0.005000! `8 ~ n* N# c+ ^& C
3 W# F: ?& z1 u
输出矩阵为：
+ T+ M+ h( T5 ~# S% R# r
5 q M: M( }5 g- Z
data_out =
/ w' ]) G( s, a, t2 K$ M
7 H' ~. U1 C8 n4 k
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
% ]! a: D [ M+ n
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000\" H [& Z\" F2 o
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
: ^* T9 s\" N8 v1 r4 P
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.0625000000000005 o o5 ~* ]4 [5 n
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
& t( X% R\" h3 Q
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000( B7 u% `( j* h0 H0 U7 B6 o; G# u( Y
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000! I; D. o! [; J2 T' u
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
4 J- s* g& ~0 t; Z8 b1 M6 k
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
9 r- q\" D+ Z! B1 ^+ G
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000+ }4 l$ |7 }1 C0 R3 y- \
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000 H* A4 s\" ^5 R% X\" T
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000, e' x, v! I* p e
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125002 _5 o( {6 M6 G8 G! g
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.0000610351562509 |; ?4 C\" B( \
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
0 X( I3 `. |) P\" }: _6 A+ s
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
. S. V' U; {2 K5 r( S( F, T M
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531, i\" H/ I+ [0 |; u! |. |
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
8 @% V' G/ \. D; S
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
' K/ T P1 @- Z! b( _
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
5 B/ _\" Y7 M9 D( C) N9 B/ J+ s
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158+ h9 K* s8 k\" I B4 n H
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579. I& g' |. |+ R- G
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290( q! ~7 r! N0 m4 I+ h1 o
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.0000000596046455 _' c* F0 h2 F; \
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322. o8 T0 \3 N\" D* k/ r
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161* m6 o/ e+ ^0 G& z
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.0000000074505815 m: F6 N2 `7 G- b
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
/ Q$ z- G0 G) `& P\" x
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
* r0 F( t* e/ r4 x\" Q1 u8 @
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.0000000009313233 i% Z% s' @) x2 ]3 Z# e# M9 K
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661, k3 D# w! l2 q' q: t1 b
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831\" P! L/ S0 y0 s1 G0 B; q. M( F
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
# h- J\" j6 t% `; m/ I$ T
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
\" j6 ?; y) e4 M6 ]' l) Q
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
9 G* G\" @, c% `) n+ P
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
% `8 q% `( F. @
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
4 ]# t/ P# I0 P) P c1 ]& m6 X/ [
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638* k9 L\" T. J' X. v+ Z
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
4 D+ k# o3 X/ ?1 M2 z' r+ }. @
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009090 s! O5 X5 v0 d6 Q% l4 ?
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.0000000000004555 e# \& `3 O; b\" Y( H+ I. J
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.0000000000002273 ~4 r4 d# Z1 Z5 a4 R' m6 ^
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
& ]' R: t+ o* N5 t3 I( k) \* T
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057& |: v\" l3 B' o d9 S
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028. ]. V5 A) t+ }1 v+ o
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014; l, s1 y6 H* S' ^( m; N; [! E
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
4 X6 m+ S# _1 R! N
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
5 h m5 n; s6 F8 P: O# o$ G3 t
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
9 }2 P) d6 i$ p. c! o/ S) q
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001, x( R7 }! P1 m1 U' O. `
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000